limit as x approaches 0+of (x^2+3x+4)/x

解答

x \to 0 + lim (\frac{x ^{2} + 3 x + 4}{x})

\infty

求解步骤

x \to 0 + lim (\frac{x ^{2} + 3 x + 4}{x})

除以分母的最高次幂:

x + 3 + \frac{4}{x}

= x \to 0 + lim (x + 3 + \frac{4}{x})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

不定型除外

= x \to 0 + lim (x) + x \to 0 + lim (3) + x \to 0 + lim (\frac{4}{x})

x \to 0 + lim (x) = 0

x \to 0 + lim (3) = 3

x \to 0 + lim (\frac{4}{x}) = \infty

= 0 + 3 + \infty

运用无穷大属性:

c + \infty = \infty

= \infty

x \to - 3 lim (x^{3} - 3 x - 7)

x \to 0 lim (\frac{e ^{x^{2}} - cos ( x )}{sin ^{2} ( x ) + 3 sin ^{5} ( x )})

x \to - 2 lim (3 x^{2} + 4)

x \to - 1 + lim (2 x + 1)

x \to 0 + lim ((1 + 5 x)^{\frac{2}{x}})